A device contains two circuits. The second circuit is a backup for the first, so the second is used only when the first has fail
ed. The device fails when and only when the second circuit fails. Let X and Y be the times (in years) at which the first and second circuits fail, respectively. Their joint probability density function (pdf) is 6e-xe-20 for 0 < x < y 〈 oo; otherwise (a) Find the pdf of X. Identify the distribution of X (b) Find the pdf of Y (c) What is the expected time at which the device fails?
1 answer:
Answer:
Step-by-step explanation:
The pdf of X is given by 3e^x(1-e^-2y). Please check the screenshot for the workings.
The pdf of Y is given by 6e^-2y. Please check the screenshot for the workings.
The expected time the device fails is the expected time Y fails, so we are going to find the expected time of Y which equals to 0.83.
Please check the screenshop for the workings. Thanks
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<u>Answer:</u>
The baseball cards remain in Nathan’s collection is 106 cards
<u>Explanation:</u>
Total number of cards Nathan has= 220
Number of cards he let his brother have = 1/4 of his collection
= = 55 cards
Number of cards he sells = 20% of his collection
=
=44 cards
No of cards he gives to his friends=15 cards
Remaining cards = total number of cards – (no of cards he gave to his brother+ cards he sold+ cards he gave to this friends)
= 220 – ( 55+44+15)
=220-114
=106 cards
baseball cards remain in Nathan’s collection is 106 cards